Though undoubtedly with the grand manner, the 11th Duke of Devonshire, who has died aged 84, was a rather mild Conservative (and sometime Social Democrat) politician and a modern, if diffident, entrepreneur, who helped to turn Chatsworth House, his magnificent stately home in Derbyshire, with its 12,000-acre estate, into a public resource, without compromising its dignity or losing it as a family home.

It would be many years before he was no longer frightened of being thought a dotty duke, after he installed an effigy of Elvis Presley, which played Rock Around The Clock when the telephone rang, claiming it to be his favourite possession.

"It has never been my line to become a circus like Woburn Abbey," said the duke in 1976. "I want to keep Chatsworth in the family. My son is very keen on taking it over when I die. So, obviously, I have to tackle the problem of going into the red."

At that time, he was proposing a scheme under which individuals would pay £50 a year (and companies £100) to visit Chatsworth at any time they wished. Both would receive inscribed certificates of membership and a car badge. The intention was to increase attendances from the existing 300,000 a year.

The reason was that the previous year panic had set in. The duke had had to sell some of the family's picture collection - it remains one of the finest in the country - to make up the shortfall in the cost of running the estate. One hundred and fifty staff were made redundant, including 11 gardeners and building workers.

Devonshire faced such problems after he succeeded his father, the 10th duke, who died suddenly in 1950 (his elder bother, William, had been killed in the second world war). Up to then, his life had been led on conventional lines for his class. He went to Eton and Trinity College, Cambridge, served in the Coldstream Guards, and won the military cross in the Italian campaign. He married one of the glitteringly idiosyncratic Mitfords, the Hon Deborah Vivian Freeman-Mitford, in 1941.

Even standing as a Conservative candidate at Chesterfield, in 1945 and 1950, was the sort of thing that might have been expected of such a young man, though his none too exciting political career did not begin in earnest until he was the 11th duke. He was parliamentary under-secretary for commonwealth relations from 1960 to 1962, minister of state at the Commonwealth Relations Office from 1962 to 1964, and for colonial affairs from 1963 to 1964. His appointments, he once said, were "the greatest act of nepotism ever" - his uncle, Harold Macmillan, was then prime minister. He later joined the SDP, although he sat as a cross-bencher in his rare appearances in the Lords.

The learning curve faced by one of the most wealthy people in Britain, owning 75,000 acres of Derbyshire, Yorkshire and Ireland, and Pratt's Club in London, was sometimes steep. He worked out a scheme under which, by putting the estates in trust, much inheritance tax would be cut out; and, 15 years ago, he even launched a scheme for saving £400,000 off his annual electricity bill by opening up a half-mile pipe which brought water into the house from three lakes on the nearby moors, generating enough current to light all the 2,084 bulbs in the chandeliers of Chatsworth.

As a young man, Devon- shire's ducal manner could sometimes seem abrasive. Labour MP Dennis Skinner attacked him in the House of Commons in 1974 because he allegedly was "very much in charge" of Eastbourne borough council. They were joint owners, with the Chatsworth Trustees, of land which had been sold for housing in 1972. The council, claimed Skinner, was very much in the duke's pocket over planning matters. The agent to the trustees of the Chatsworth estate denied the allegations.

Even in later years, the duke's disputes with ramblers, who used the paths near his home, did not bring him the sort of publicity most stately-home owners would have welcomed. But by the time he had grown into the grand old man of stately homes, the aristocrats' aristocrat and a man who could be humorously self-deprecating about himself and his own place in the world, even the ramblers had been disarmed.

He signed an agreement in 1991 with the Peak National Park Authority which opened up 1,300 acres of his estate to walkers. He said that everyone was "welcome in my back garden". The fact that he was a walker himself, despite a painful hip condition, made for further public sympathy; the fact that he had been a president of the Polite Society, and invariably followed its rules, was also an asset.

"The key to my life was the army," he said. "It turned me from a filthy, useless boy into something vaguely approaching a man. All Cavendishes are lazy by nature, and my entire life has been a battle against indolence. When you consider my advantages - there probably isn't anybody more fortunate in the world - I've achieved absolutely nothing. It's quite shaming." He is likely to go down in history as an English gentleman in every sense of the term.

He is survived by his wife, the Duchess of Devonshire, his son, the Marquess of Hartington, who becomes the 12th duke, and his two daughters.

Phillip Whitehead writes: No duke of Devonshire in the long Chatsworth dynasty belonged as much to Derbyshire as this one. Alert, diffident, putting his wealth and his influence behind a myriad of good causes, he lived in a state of grace that dukes can rarely achieve. Andrew and Deborah Devonshire let us feel that, far from them owning much of the county, it owned them, and their great palace on the Derwent.

I last saw Andrew a few weeks ago, freshly out of hospital, but determined to thank a visitor (Liz Forgan) for her help with a project he had inspired for a generation, the Arkwright Society. He just made it to the door as we left, standing with difficulty in the wintry sun: no fuss, no self-pity, just an immense courtesy that endured to the end.

· Andrew Robert Buxton Cavendish, 11th Duke of Devonshire, born January 2 1920; died May 3 2004